Toward a consistent random phase approximation based on the relativistic Hartree approximation

We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e’) quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces ${\mathit{m}}^{\mathrm{*}}$/m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e’) data.